Apparatus for providing variable impedances



May 23, 1961 o. PATTERSON APPARATUS FOR PROVIDIIQG VARIABLE IMPEDANCESOriginal Filed July 30, 1951 LAY 2 Sheets-Sheet 1 HIGH GAIN DIFFERENTIALAMPLIFIER DIFFERENTIAL AMPLIFIER INVENTOR. OMAR L. PATTERSON BYWIZJQVKA? ATTORNEYS May 23, 1961 o. L. PATTERSON 2,985,372

APPARATUS FOR PROVIDING VARIABLE IMPEDANCES Original Filed July 50, 19512 Sheets-Sheet 2 FUNCTION 208 E 2'4; 'E-F(EX) E GENERATOR X i ZLJ I.

SUBTRACTION MULTIPLICATION J CIRCUIT I b cIRcuIT F(E E-K-E-F(- I X q:.F( F

FIG. 4. c -g-c K F(E I ll A CATHODE FOLLOWER OF I 0w OUTPUT IMPEDANCE 0FIG. 6.. A ,20I HIGH GAIN c B DIFFERENTIAL i Am-LIFIER g 203 INVENTOR.

\zos 3 OMAR L. PATTERSON 3 KEG 2 E a, FIG. 5 7

United States Patent APPARATUS FOR PROVIDING VARIABLE IIVIPEDANCES OmarL. Patterson, Media, Pa., assignor to Sun Oil Company, Philadelphia,Pa., a corporation of New Jersey Original application July '30, 1951,Ser. No. 239,279. Divitled and this application Sept. 22, 1952, Ser. No.310, 02

4 Claims. (Cl. 235-184) This invention relates to computing circuits andhas particular reference to the provision of circuits for providingvariable impedances.

This application is a division of my prior application Serial No.239,279, filed July 30, 1951 (Patent No. 2,855,145). Reference may alsobe made to my prior applications Serial Nos. 130,270 (Patent No.2,727,682) and 196,480 (Patent No. 2,788,938), filed respectivelyNovember 30, 1949 and November 18, 1950. The present application is inpart a continuation of said application Serial No. 196,480.

One of the objects of the present invention is the provision of animpedance which may be controlled as a function of a potential or oftime so as to vary in accordance with the output of a functiongenerator. More particularly, there is provided a functional capacitanceor an arrangement in which a charge may be functionally varied independence on an independent variable represented by a potential.

A further object of the invention is the provision of variableimpedances of high value. In particular, in accordance with this phaseof the invention, there may be provided continuously variablecapacitances of high capacity values far exceeding those obtainable withmechanically variable condensers.

These and other objects of the invention, particularly relating todetails of construction and operation, will become apparent from thefollowing description read in conjunction with the accompanyingdrawings, in which:

Figure 1 is a wiring diagram of a high gain differential amplifier usedto form an element of the circuits provided in accordance with theinvention;

Figure 2 is a diagram showing a high accuracy subtraction circuitinvolving the use of the high gain differential amplifier of Figure 1;

Figure 3 is a multiplication and division circuit utilizing the highgain differential amplifier of Figure 1 and used in the circuitsprovided in accordance with the present invention;

Figure 4 is a diagram showing the construction of a circuit whichprovides an impedance varying as the function of an independent variableor, alternatively, which may be used for the provision of a chargevarying as the function of an independent variable;

Figure 5 is a diagram showing a cathode follower circuit having very lowoutput impedance and utilizing a high gain differential amplifier of thetype illustrated in Figure 1; and

Figure 6 is a diagram showing a water drive network suitable for use inan oil reservoir analyzer and specifi- 'ice cally incorporating meansproviding continuously variable capacitances of high value.

In accordance with the invention there is utilized a high gaindifferential amplifier providing high accuracy of circuits of computingtype in which it is incorporated and independence of tubecharacteristics. Such a differential amplifier will first be described.

A preferred form of high gain differential amplifier is illustrated inFigure l and is of the type described in Vacuum Tube Amplifiers, volume18, Radiation Laboratory Series, page 485, McGraw-Hill, 1948. It will benoted that this differential amplifier is, in many respects, similar tothat disclosed in my application, Serial No. 196,480. It involves animprovement thereover in the provision of a constant current triode.

A pair of triodes 2 and 4 have their grids connected to the inputterminals A and B. These triodes are provided with anode load resistors6 and 8 and their cathodes are connected together and to the anode of atriode 10 arranged in a cathode follower circuit, there being providedthe cathode load resistor 12. A battery 14 or other source of fixedpotential is connected between the remote end of the cathode resistor 12and the grid of triode 10.

The grids of a pair of triodes 16 and 18 are respectively connectedthrough resistances 32 and 34 to the anodes of triodes 4 and 2. Theanode of triode 16 is connected directly to the positive potentialsupply line. The anode of triode 18 is connected to the same supply linethrough a load resistor 22. The cathodes of triodes 16 and 18 areconnected to each other and to a common cathode load resistor 24 whichis, in turn, connected to a negative potential supply line. To this linethere is also connected the contact of a potentiometer 26 which isconnected respectively through resistances 28 and 30 to the grids oftriodes 16 and 18. An output triode 36 is connected in a cathodefollower circuit, its cathode being connected to the negative potentialsupply line through a resistor 38 and a resistance-capacitance networkindicated at 40. Feedback is provided through resistance 41 to the gridof triode 16. The grid of triode 36 is connected to the anode of triode18 and the anode of triode 36 is connected to the positive potentialsupply line. The output terminal C is connected to the cathode of triode36.

With a balancing adjustment properly made at potentiometer 26, theaction of this differential amplifier is to provide at the outputterminal C a potential E which is related to the input potentials atterminals A and B, namely E and B in accordance with the expressiongiven below the circuit diagram in Figure 1. By virtue of theamplification which is provided in the circuit, the constant a has avalue greatly exceeding unity and, in fact, with a proper choice ofcircuit constants, this factor may have a value as high as 10,000.

In the case of the differential amplifier circuit illustrated anddescribed in said Patterson application, Serial No. 196,480, thecathodes of the triodes corresponding to 2 and 4 are connected to thenegative supply line through a resistor. When such a connection is made,the expression of E contains an additional term involving the sum of thepotentials E and E This common mode of these potentials is substantiallycompletely eliminated by the provision of the triode 10 and itsconnections in place of a fixed resistance, the action of this triodebeing to aesaeva provide a constant total current from the cathodes oftriodes 2 and 4. As will be evident, this constant current conditionresults from the fact that the cathode potential of triode with respectto the lower end of resistor 12 is maintained substantially constant bythe provision of the battery 14, the positive terminal of which isconnected to the grid of triode 10. It will be evident, therefore, thatif the triodes 2 and 4 are similar in their characteristics, as theydesirably should be, a simultaneous change of potential of the grids ofboth in the same sense and amount will result in no change of thecurrents through the load resistors 6 and 8 and, consequently, no outputsignals to the grids of the triodes l6 and 18. When, therefore, thetriodes 2 and '4- are similar to each other and the triodes 16 and 18are also similar to each other, and minor differences are subjected tosubstantial elimination by adjustment at potentiometer 26, theexpression given below the circuit diagram holds to a high degree ofaccuracy and the output potential is extremely sensitive to diilerencesbetween the input potentials. As will appear hereafter, this conditionmay be utilized in securing a high precision of equality between variouspotentials, in view of the high value of the factor ,u. The highnumerical value of this factor may be also utilized to secure ratios, aswill appear hereafter, which are very nearly equal to unity.

A highly important feature of the difierential amplifier as a basiccomputer element, especially for long time operation, is mutualcancellation of effects of heater voltage variation and aging of tubecharacteristics.

In one embodiment of the present invention there is utilized asubtraction circuit which will now be described.

In this subtraction circuit the high gain differential amplifier ofFigure l is indicated at 42, its terminals A, B and C being indicated inFigure 2 to correspond with those in Figure 1. The terminal B isconnected to the junction of a pair of resistors 44 and 46 whichinitially may be considered to have the same resistance value R Theterminal A is similarly connected to the junction of a pair of resistors48 and 50 which may also be assumed to have the same resistance value RThe upper end of resistor 48 is connected to a terminal G, while thelower end of resistor 50 is grounded. The upper end of resistor 44 isconnected to a terminal H, while the lower end of resistor 46 isconnected both to the terminal C and an output terminal I. Terminals Gand H constitute input terminals for the subtraction circuit. That theoutput potential E appearing at terminal I is very precisely equal tothe difference of the input potentials E and E appearing at terminals Gand H will be evident from consideration of the expressions given belowthe circuit diagram in Figure 2. When the value of ,u. is very large, aspreviously described, it will be evident that the fractional factorinvolved in the last line of the expressions is very nearly equal tounity. Accordingly, an output potential is provided which issubstantially equal to the difference of the input potentials. It willbe evident that, even though the value of [.6 may vary from one highgain differential amplifier to another, or during the use of anamplifier because of changes in tube characteristics, the subtractioncircuit output is highly independent of any such variations of operatingcharacteristics of the differential amplifier. The circuit is alsocapable of handling a very wide range of both positive and negativepotentials.

In particular, it is to be noted that this subtraction circuit does notinvolve any additive term derived from tube potentials or other sourceas do subtraction circuits heretofore known. This fact is particularlyimportant in uses of the subtraction circuit for integration ordifferentiation.

One embodiment of the present invention utilizes a multiplicationcircuit which will now be described with particular reference to Figure3, the high gain differential amplifier of Figure 1 being indicated at74.

A pair of triodes 76 and 78 have their anodes connected to a positivepotential supply line 79 the potential of which will be designated E Thecathodes of these triodes are connected to the ends of the resistance ofa potentiometer 80, the contact of which is connected to the anodes ofthe triodes 82 and 84 of a second pair, the cathodes of which areconnected to the ends of a potentiometer 86, the contact of which isgrounded. Equal resistances 88, 9t}, 92 and 4 are connected to the gridsof the respective triodes and join them to various terminals. Theseresistances should have quite large resistance values, for example, tenmegohms. The resistance 88 connects the grid of triode 76 to a terminalP. The resistance 92 connects the grid of triode S2 to a terminal K. Theresistance 94 connects the grid of triode 84 to a terminal L.

A pair of equal resistances 96 and 98 connect the positive supply line79 to ground to provide at a terminal 100 a potential which is one-halfthe potential of the positive supply line. A pair of equal resistances102 and 104 connect the positive potential supply line 79 to theterminal C of the high gain differential amplifier 74. The junction ofresistances 102 and 104 is connected to the grid of triode 78 throughthe high resistance 90. Terminal B of the differential amplifier isconnected to the contact of potentiometer 80. Terminal A of thedifferential amplifier is connected to the junction of equal resistances106 and 198 which are connected between the positive supply line '79 andground to provide at their junction a potential equal to one-half thepotential of the supply line.

' 'Ihe triodes 76, 78, 82 and 84 are desirably of the same type and ofclosely similar characteristics. The resistances involved atpotentiometers and 86 are small and the grids of the triodes are eitherslightly positive or negative with respect to their cathodes underoperating conditions depending upon the tube type used. As is known, forlow absolute values of potential of a grid with respect to the cathodefor which grid current flows and for low grid current, an exponentialrelationship between the grid current and grid-cathode potential exists.If each of the grid input resistors is large, as stated above, and eacheffective cathode resistor is small, it may be readily seen that thegrid-cathode potential of each of the triodes is, to a good degree ofaccuracy, proportional to the logarithm of the input potential plus aconstant deendent almost solely on the grid input resistance.

As will be evident from the circuit arrangement, the sum of the currentflowing through the triodes 76 and 78 is equal to the sum of thecurrents flowing through the triodes 82 and 84. Assuming first identicalcharacteristics of the triodes and location of the potentiometercontacts at the centers of resistances 80 and 86, and assuming furtherequality of resistances at 80 and 86, it will be noted that the functionof the differential amplifier 74 is to maintain at terminal B the fixedpo tential which exists at terminal A and which is one-half thepotential of the positive supply line. The differential amplifierenforces this condition by providing at terminal C a control of thepotential of the grid of triode 78. The potential to ground existing atthe junction of the equal resistances 102 and 104 will be noted to beone half the potential to ground appearing at the terminal C plusone-half the potential of the positive supply line above ground.Accordingly, the potential which is enforced between the junction ofresistances Hi2 and 304 and terminal B of the difierential amplifier isone-half the potential at terminal C. Noting that the effective inputpotential E at terminal P is referred to terminal which in turn isone-half the potential of the positive supply line above ground, it willbe evident that the enforced conditions are as given in the equationbeiow the circuit diagram of Figure 3, i.e., the product of theeffective input potentials to the triodes 76 and 78 is equal to theproduct of the input potentials to the triodes 82 and 84. What arereferred to as the effective input potentials to triodes 76 and 78 are,of course, the potentials measured above the datum furnished by theterminal 100 and terminal B of the differential amplifier. The resultis, accordingly, that terminal C provides an output which isproportional, with a factor of 2, to the product of the potentials B andE divided by the potential E It will be noted that in the foregoingcircuit the plate voltages are held substantially constant andfurthermore the sum of the currents through the upper triode pair isalways equal to the sum of the currents through the lower triode pair.Consequently, both the upper and lower pairs are operating undersubstantially identical conditions of input potential products. A changeof heater voltage or drift in tube characteristics tends to cancel out.Reference was made above to the use of triodes of substantiallyidentical characteristics. While this is desirable, it is not essentialand the adjustments at potentiometers at 80 and 86 may be made to takecare of differences in the tubes and in addition may be used to provideadjustment of exponents of the factors.

While only two tubes are illustrated in Figure 3 in each of the upperand lower groups, it will be evident that, if desired, additional tubesmay be arranged in parallel withthese to provide additional factorsappearing in either the numerator or denominator of the value of theoutput potential, or in both. Thus, the quotient of any number offactors may be provided. Desirably, however, the number of tubes usedshould be equal in the upper and lower groups to provide substantiallyidentical operating characteristics; but, obviously, this introduces nodifficulty inasmuch as any one or more of the tubes may have a constantpotential input which will then appear merely as a scale factor in theresult.

The circuit of Figure 3 is particularly desirable for multiplication inwhich case E will be merely a constant potential and will appear as ascale factor in the result.

In accordance with the present invention there is provided, utilizingthe circuits described above, a circuit adapted for the production of afunctional capacitance, i.e., a capacitance which varies as a givenfunction of a variable and which may be, for example, time or somearbitrary or scheduled potential. Use for such a capacitance arise attimes in the matter of formulation of analogs. The capacitance thusrequired may be either positive or negative or may well vary betweenpositive and negative values. A circuit of this type is illustrated in.Figure 4.

At 202 there is indicated a terminal between which and ground thefunctional capacitance is to be provided. At 294 there is indicated afunction generator which may be of one of the types described inPatterson application, Serial No. 188,291, filed October 4, 1950, or inPatterson and Yetter application, Serial No. 239,278 (Patent No.2,793,320), filed July 30, 1951. As pointed out in said applications, aninput potential E which may be assumed applied to a terminal 296 willgive rise at an output terminal, indicated at 208, to a potential whichis some arbitrary predetermined function of the potential E which outputis here designated as HE The output potential at 208 is delivered to theterminal L of a multiplication circuit 210 such as that of Figure 3, theother two terminals K and P of which are indicated. To the terminal Kthere is delivered the potential E from the terminal 262.

The output terminal P of the multiplication circuit 210 delivers to theinput terminal H of the subtraction circuit 212 of the type illustratedin Figure 2 a potential as indicated in Figure 4 which is a product ofthe potential E and the functional potential from the function generatormultiplied by a constant K which is, of course, subject to adjustment.To the terminal G of the subtraction circuit the potential E is appliedfrom the terinitial 202 with the resulting output at J of the difierence6 potential as indicated in Figure 4. Between the terminals 202 and Ithere is connected the physical capacitance 214 having a value C and, inmany cases, desirably adjustable.

The two equations following the diagram in Figure 4 indicate the natureof the derivation of the apparent capacitance between terminal 202 andground. The first equation gives the charge which exists on thecondenser 214, this charge being the product of the actual capacity ofthis condenser and the potential between its terminals. The apparentcapacity between terminal 2G2 and ground C is then given by the quotientof this value of q and the potential E between the terminal 202 andground and it will be evident that this ap parent capacity is theproduct of C and K with the function generated by the functiongenerator. C and K, both or either of which may be adjustable, merelydetermine the scale factor involved. It will be evident that thefunction may be applied negatively to the terminal L and, consequently,the apparent capacitance may be either positive or negative. Even moregenerally, the function may vary through zero in which case the apparentcapacitance may also vary through zero. In this connection, it should benoted that, generally speaking, it is the dynamic value of suchcapacitance which is of interest so that no loss of generality of resultis occasioned by the addition of constant potentials such as may berequired to provide a range through zero of operation of the circuitcomponents.

Sometimes, there is required rather than a functional capacitance aunctional charge, that is, a charge appearing between terminals whichvaries as a function of some variable for example either time or somepotential which may be dependent upon some other variable. Such afunctional charge may be readily obtained by what amounts to asimplification of the circuit illustrated in Figure 4 by omission of themultiplication circuit and the delivery from terminal 208 of thefunction generator directly to terminal H of the subtraction circuit ofthe function which is generated by the generator. In such case it willbe evident that the apparent charge appearing between terminal 262 andground will be that of the first expression below the circuit of Figure4 with the value of E equal to unity. A positive sense of charge is thussecured. However, if instead of the subtraction circuit, there isprovided an addition circuit of any of the various known types, then thevalue of the charge q will be numerically the same but of negative sign.

It will be further evident that special cases of function generationwill give rise to particular types of apparent capacitances of specialutility. E may, for example, well be E, in which case the capacitance(or charge) may be an arbitrary function of E. In this case, of course,the multiplication circuit may Well be omitted, the output of thefunction generator being applied directly to terminal H of thesubtraction circuit. But the sub traction circuit may also be omitted ifa suitable function is generated, so that, still more simply, thefunction generator may have its output connected directly to the lowerterminal of condenser 214. Such connection will generally involve acathode follower type of amplifier of low output impedance such asdescribed hereafter.

It may also be noted that while a capacitance is indicated at 214, thisis merely representative of a general impedance which may be quitearbitrary, being, for example, a resistance, inductance, any combinationof resistance and reactance elements, a transmission line having lumpedor distributed parameters, or the like. In general, such an impedancemay be made functionally dependent upon a potential.

Of particular importance, however, is a circuit capable of providing acontinuously variable capacitance of high capacity value. Structuralsize seriously limits the capacity of variable condensers. Butoccasionsarise where large variable capacities are called for and thebest that aeaasva could heretofore be provided involved the use of setsof condensers selectively switched to provide steps of change. Inaccordance with the present invention there may be provided acontinuously variable capacitance of high capacity value.

Involved as an element of such capacitance is, desirably, a cathodefollower of low output impedance which will now be described.

A high gain differential amplifier of the type shown in Figure 1 isindicated at 201 in Figure 5. The terminal C is connected to groundthrough the resistance 2% of a potentiometer, the adjustable contact ofwhich is connected at 205 to terminal B. The result is to apply atterminal B a potential which is K times that at C, K being equal to orless than unity. It will be evident that for an input at A there will beprovided at C an output given by the second equation of Figure 5. If ,uis large, as described above, K is substantially the factor ofproportionality, being unity if terminal C is directly connected toterminal B.

The advantages of this circuit lie in its extremely low output impedanceand its high degree of independence of tube characteristics. For thesereasons it is of general utility; for example, it may be used to drivelow impedance devices, such as speaker coils without the use of atransformer.

Furthermore, it may be noted that the circuit in Fi ure 5 provides ahigh precision linear amplifier having a definite gain set by the valueof K which depends only on the values of the resistances appearing aboveand below the potentiometer contact. These resistances may be accuratelyfixed by the use of precision resistors joined to a terminal replacingthe potentiometer contact.

The arrangement for providing a variable capacitance is illustrated inFigure 6 embodied in a water drive analog the utilization of which ismore fully described in my application Serial No. 196,480. Saidapplication illustrates and describes a variable capacitance arrangementwhich is similar to that about to be described except for the differenceinvolved in the cathode follower portion of the circuit.

The water drive analog comprises a series of resistances 209, thejunctions of which are connected to ground through capacity elementswhich are indicated at 267. In view of the fact that these capacityelements require a wide range of adjustment and relatively high capacityvalues, there are used in this network dynamic capacity elements whichare similar to each other so that only one of these is detailed at 207,it being understood that all of the individual elements 207 areconstructed as i1 lustrated at 207'. The resistances 209 of the networkare shown as variable but, in practice, there are preferably used,instead of continuously variable resistors, sets of resistors which arechosen into the circuit by switching. In the same fashion, the condenser213 is shown as variable but since these condensers 213 are ofrelatively large capacity values in the particular use here illustrated,it is preferable in actual practice to utilize groups of fixedcondensers which are selectively switched into the circuit. It is alsogenerally desirable to provide resistance anud capacity units which may,as a whole, be switched into and out of the circuit. However, suchdetails are arbitrary and are not illustrated. Generally, for goodreproduction of an actual water drive network, a considerable number ofnetwork sections is involved. There may, for example, be fifteen or moreof these sections, and the multiplicity is indicated by the use ofdotted lines in the showing of the network.

Referring now particularly to the capacitance element indicated at 207(which also includes a charging arrangement), it will be noted that eachsuch element comprises a condenser 213 connected to the correspondingjunction between resistances 209 of a pair. The value of the capacityprovided by the condenser 213 may be alternatively divided ormultiplied. The range for each condenser, for example, may be from aboutone-tenth to about fifty times its capacity value and it will beevident, therefore, that by the use of a limited number ofinterchangeable condensers, a very large range of capacities may beprovided. As will appear, the adjustments of capacity are continuous. Itis not necessary in practice to have the resistances of the networkcontinuously variable so that a reasonable number of fixed resistancesmay be provided and switched into the circuit as indicated above.

The upper terminal of the condenser 213 is connected to the grid of atriode 15 in a cathode follower arrangement, there being providedbetween the cathode and ground a potentiometer resistance 217 associatedwith a variable contact 219. This variable contact arrangement pro'videsbetween the contact 219 and ground a potential varying fromapproximately the value of the potential between the grid and ground tosome limiting fraction thereof as, for example, one-tenth the value ofthe grid potential. A condenser 221 connects the contact 219 to the gridof an amplifying triode 223. This triode is associated with an anodeload resistor 22S and the cathode is connected to ground through acathode resistor 225. The amplification of the amplifier just describedmay be set by a proper choice of the cathode resistor 225'. Thisamplificatio'n may vary, for example, from unity to about fifty. Theanode of triode 223 is connected to a contact 227 engageable by a switcharm which is alternatively engageable with contact 229 connected to thepotentiometer contact 219.

Considering the arrangement so far described, assume that the switchengages contact 229. It will then be evident that at the switch therewill appear a potential which may vary from approximately the value ofthe potential of the grid of triode 215 to some small fraction thereofdepending upon adjustment of potentiometer contact 219. Division of thepotential appearing at the grid of triode 215' is thus efiected, thepotential of the switch being of the same sign as that of the grid. Onthe other hand,

if the switch engages contact 227 the output at the potentiometercontact 219 is amplified to the degree afiorded by the amplifierincluding triode 223 and the potential appearing at the switch will beof a sign opposite that appearing at the grid of triode 215, or, inother words, the

phase of the input is reversed. In short, considering both adjustmentsof the switch, the inphase output of the arrangement may be any chosenfraction of the input or, alternatively, the out-of phase value of theoutput may be either a fraction or a multiple of the input. As will beevident from consideration of the use of the network being described inan analog, a repetition cycle is involved so that only alternatingsignals need be considered, these being delivered from the switchthrough condenser 231.

A cathode follower of low output impedance is illus trated at 233 andmay be of the type shown and described with reference to Figure 5.Alternatively, for many purposes, it is sufiicient to use a cathodefollower of less accurate type and of somewhat higher output impedancesuch as described in my application, Serial No. 196,480. Considering,however, that the cathode follower at 233 is of the type illustrated inFigure 5, the condenser 231 provides its output to terminal A and thecathode follower output at terminal C is connected through line 235 tothe lower terminal of condenser 213.

The cathode follower provides a very accurate correspondence of input tooutput potential irrespective of out put current drain by reason of itslow output impedance. The condenser 213 constitutes a load on thecathode follower circuit and it is very important that the output shouldbe linearly related to a high degree of accuracy to the input in orderthat the effective dynamic capacity will be constant irrespective of thecharges or currents which are involved. This last result cannot besecured to 9 a sufficient degree of accuracy with an ordinary cathodefollower and, hence, there is used the cathode follower circuit ofFigure or such a cathode follower circuit as is described in said priorapplication Serial N0. 196,480.

That the arrangement above described constitutes a continuously variablecondenser may now be made clear. If the switch engages contact 229, thepotential fed to the lower terminal of condenser 213 will be of the samesign as the potential fed to the upper terminal of this condenser sothat there -will appear across the condenser 2213 a potential which issome fraction of the potential between its upper terminal and ground.Accordingly, there is secured an effective capacity having a fraction ofthe capacity of the condenser 213, the value of this fraction beingdetermined by the setting of potentiometer contact 219 and beingcontinuously variable with the continuous variation of this contact. Onthe other hand, consider .the switch in engagement with contact 227.There is then applied to the lower terminal of the condenser 213 apotential which is of opposite phase with respect to the potentialapplied to the upper terminal of this condenser and this potentialapplied to the lower terminal may be either a fraction or a multiple ofthe potential applied to the upper terminal depending upon the choice ofresistance 225' and the setting of the potentiometer contact 219.Accordingly, the potential across the condenser will exceed thepotential of its upper terminal with respect to ground and thispotential across the condenser will be continuously variable withadjustment of contact 219. In view of this, it will be evident that thesystem provides what amounts to a multiplication of the capacityappearing between the upper terminal of condenser 213 and ground ascompared with the physical capacity of the chosen condenser at 213.

The dynamic capacity afforded by the arrangement just described is ofquite general applicability. The potentiometer in the cathode circuit oftriode 215 may be directly calibrated in terms of continuous variationsof capacitance and, in view of the fact that a large condenser of highgrade and small leakage, for example, of the order of two microfarads ormore, may be provided at 213, it will be evident that there may beprovided an adjustable capacitance which may have an effective capacityof the order of several hundred microfarads. Such a dynamic capacitancemay be used, fo'r example, for filtering. Furthermore, in view of theinherent negative feedback involved, there is a very low effectiveseries resistance so that, when used as a filter, low impedancefiltering will not be impaired.

This is in contrast with the normal difiiculty of securing highcapacitances without leakage and, of course, of securing continuousvariability of capacitances of high value.

The remaining portion of the appratus indicated at 207 has to do withthe initial charging of the capacitances in the network prior to a zerotime of the repetitive cycle of an analyzer or analog such as describedin said appli cation, Serial No. 196,480.

The charging is effected through a triode indicated at 237 which has itscathode connected through resistance 239 to the upper terminal ofcondenser 213. The grid of triode 237 is connected through resistance241 to the contact of a potentiometer 243 which is connected between thepositive potential supply line and ground. The grid of triode 237 isconnected through condenser 249 to the cathode of a triode 245 in acathode follower arrangement including the cathode load resistor 247.The grid of triode 245 is connected to a terminal 251 which, as willappear from said application Serial No. 196,480, is connected to asource of positive square waves of a timing circuit, the applied wavehaving a duration, for example, of 2000 microseconds in a preferredarrangement of the apparatus.

In view of the presence of condenser 249, it will be evident that thegrid of triode 237 is subjected to a potenanswers tial which varies as asquare wave about a constant po tential set by the position of thecontact on potentiorneter 243. The square wave is of accuratelyregulated amplitude and it will be evident that during the positivecycles of this wave the potential at the grid will be positive so thatthe triode 237 will be conducting and will charge the condenser 213, orrather the effective dynamic capacitance which has been described, to apotential at its upper terminal with respect to ground corresponding tothe sum of the potential of the potentiometer contact and half thecomplete amplitude of the square wave, the current carrying capacity oftriode 237 being sufficient to permit full charging during the positivehalf cycle of the square wave. On the other hand, during the negativehalf cycle of the square wave, the grid of triode 237 will be driven tocut off and the network will then deliver current through the withdrawalcircuit of the type described in said prior application.

While the elements including and to the right of condenser 249 areindicated as repeated in each of the assemblies 207', in practice, suchrepetition is unnecessary and this portion of the circuit may beprovided only once for a group of the assemblies 207. In such case, thetriode 245 must be provided with adequate current carrying capacity and,to this end, the single triode indicated at 245 may be replaced by twoor more triodes connected in parallel.

The terminal 211 is the output terminal of the network and is connectedas described in said application, Serial No. 196,480.

It will be evident that various changes may be made in the embodiment ofthe invention without departing from the scope thereof as defined in thefollowing claims.

What is claimed is:

1. Apparatus for providing an effective impedance between a pair ofterminals varying as the function of a predetermined signal comprising aphysical impedance having a terminal connected to one of said pair ofterminals, and means providing between the other of said pair ofterminals and another terminal of said impedance a potential varyingwith said signal, said means including a subtraction circuit havingfirst and second input terminals and a third output terminal andoperative to produce at said third terminal a potential approximatelyequal to the difference of potential between the first terminal and thesecond terminal, said first terminal of the subtraction circuit beingconnected to the first mentioned of said pair of terminals, and saidsecond terminal of the subtraction circuit receiving a potential varyingwith said signal, the third terminal of said subtraction circuitproviding the first mentioned potential.

2. Apparatus for providing an effective impedance between a pair ofterminals varying as the function of a predetermined signal comprising aphysical impedance having a terminal connected to one of said pair ofterminals, and means providing between the other of said pair ofterminals and another terminal of said impedance a potential varyingwith said signal, said means including a function generator and asubtraction circuit having first and second input terminals and a thirdoutput terminal and operative to produce at said third terminal apotential approximately equal to the difference of potential between thefirst terminal and the second terminal, said first terminal of thesubtraction circuit being connected to the first mentioned of said pairof terminals, and said second terminal of the subtraction circuitreceiving a potential from said function generator varying with saidsignal, the third terminal of said subtraction circuit providing thefirst mentioned potential.

3. Apparatus for providing an effective impedance between a pair ofterminals varying as the function of a predetermined signal comprising aphysical impedance having a terminal connected to one of said pair ofterminals, and means providing between the other of said pair ofterminals and another terminal of said impedance a potential varyingwith said signal, said means including a function generator, amultiplication circuit having two input terminals and an output productterminal and a subtraction circuit having first and second inputterminals and a .third output terminal and operative to produce at saidthird terminal a potential approximately equal to the difference ofpotential between the first terminal and the second terminal, said firstterminal of the subtraction circuit being connected to the firstmentioned of said pair of terminals, and said second terminal of thesubtraction circuit receiving a potential from said output productterminal varying with said signal, the third terminal of saidsubtraction circuit providing the first mentioned potential, saidmultiplication circuit having one input terminal receiving the output ofsaid function generator, and having its other input terminal connectedto the first mentioned of said pair of terminals.

4. Apparatus for providing an elfective impedance between a pair ofterminals varying as the function of a predetermined signal, whichsignal is independent-of the potential between said terminals,comprising a physical impedance having a terminal connected to one ofsaid pair of terminals, and means including a function generatorproviding between the other of said pair of ten.- minals and anotherterminal of said impedance a potential given substantially by E-K-E-F(Ewherein E is the potential between the first mentioned terminals, K is aconstant, and F(E is a function of said signal.

References Cited in the file of this patent UNITED STATES PATENTS2,078,792 Fitz Gerald Apr. 27, 1937 2,423,754 Bruce July 8, 19472,472,464 -Bruce June 7, 1949 2,721,908 Moe Oct. 25, 1955 Neher Dec. 27,1955 OTHER REFERENCES

